Explain The Following Postulates And Theorems Of Geometry Flashcards

Segment Addition Postulate two segments add up to one bigger segment Angle Addition Postulate two angles add up to one bigger angle Postulate 5 a line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in one line Postulate 6 Through any two points there is exactly one line. Postulate 7 Through any three points there is exactly one plane, and through any three collinear points there is exactly one plane. Postulate 8 if two points are in a plane, then the line that contains the points is in that plane. Postulate 9 If two points intersect, their intersection is a line. Theorem 1-1 If two lines intersect, then they intersect in exactly one point. Theorem 1-2 Through a line and a point not in the line there is exactly one plane. Theorem 1-3 If two lines intersect, then exactly one plane contains the lines. Addition Property If a = b, and c = d then a + c = b +d Subtraction Property If a = b and c = d then a - c = b - d Multiplication Property If a = b, then ca =cb Division Property If a = b, then a/c = b/c Substitution Property if a = b, then a or b can be substituted for the other in any equation or inequality. Reflexive Property a = a Symmetric Property If a = b, then b = a. Transitive Property If a = b, and b = c, then a = c. Midpoint Theorem If M is the midpoint of AB, then AM = 1/2AB Angle Bisector Theorem If BX is the bisector of <ABC, then m<ABX = 1/2<ABC Definition of vertical angles vertical angles are congruent Definition of Perpendicular Lines if lines form congruent adjacent angles or right angles corresponding angles corresponding angles are congruent alternate interior angles alternate interior angels are congruent. SSI angles same side interior angles are supplementary definition of perpendicular lines If a transversal is perpendicular to one of two paralell lines then it is perpendicular to the other one too. 5 ways to prove two lines are parallel 1. show that corresponding angles are congruent 2. show that alternate interior angles are congruent 3. show that same side interior angles are supplementary 4. show both lines are perpendicular to a third line 5. show that both lines are parallel to a third line Theorem 3-8 through a point outside a line, there is exactly one line parallel to the given line. Theorem 3-9 Through a point outside a line, there is exactly one line perpendicular to the given line. Theorem 3-10 Two lines parallel to a third line are parallel to each other. Corollary If two angles of a triangle are congruent to two angles of another triangle, then the triangles are congruent.